Checks and convergence assessment for IS/AMIS with INLA
9/2/2021
Toy
##
## INLA-IS
##
## Posterior means:
## [1] 0.9301271 -0.9880918
##
## Posterior covariance:
## [,1] [,2]
## [1,] 0.132599816 -0.004151681
## [2,] -0.004151681 0.130064375
##
## Sample size (to estimate the mean)
## [1] 9137.7
##
## Sample size (to estimate the variance)
## [1] 3675.384
##
## Sample size (to estimate the kurtosis)
## [1] 5893.742
##
## L2 discrepancy
## [1] 0.003071926
##
## Sample size (per variable)
## [1] 8124.978 7555.027##
## INLA-AMIS
##
## Posterior means:
## [1] 0.9354200 -0.9824848
##
## Posterior covariance:
## [,1] [,2]
## [1,] 0.128952952 -0.005238025
## [2,] -0.005238025 0.132484218
##
## Sample size (to estimate the mean)
## [1] 9618.056
##
## Sample size (to estimate the variance)
## [1] 9087.699
##
## Sample size (to estimate the kurtosis)
## [1] 9265.605
##
## L2 discrepancy
## [1] 0.001992765
##
## Sample size (per variable)
## [1] 8510.857 8476.343
Lasso
##
## INLA-IS
##
## Posterior means:
## [1] -0.08856204 0.26010748 0.08248470 0.09992697 0.01505261
##
## Posterior covariance:
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.0021179696 -0.001089102 -0.0011607633 8.846117e-04 -1.107666e-03
## [2,] -0.0010891018 0.004282455 0.0017398917 -1.402262e-03 -1.391188e-03
## [3,] -0.0011607633 0.001739892 0.0012629344 -8.978626e-04 -1.483391e-04
## [4,] 0.0008846117 -0.001402262 -0.0008978626 6.890096e-04 8.521568e-05
## [5,] -0.0011076656 -0.001391188 -0.0001483391 8.521568e-05 1.712434e-03
##
## Sample size (to estimate the mean)
## [1] 3.714073
##
## Sample size (to estimate the variance)
## [1] 1.515723
##
## Sample size (to estimate the kurtosis)
## [1] 1.655757
##
## L2 discrepancy
## [1] 0.518793
##
## Sample size (per variable)
## [1] 4.232757 3.655277 4.726924 2.982445 5.031430##
## INLA-AMIS
##
## Posterior means:
## [1] -0.007289224 0.168143956 0.028726525 0.073246574 0.202813278
##
## Posterior covariance:
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.0065593662 -0.004448723 0.0001756576 -0.0008563857 -0.0010981170
## [2,] -0.0044487235 0.013241012 0.0014917896 -0.0042806420 -0.0046288830
## [3,] 0.0001756576 0.001491790 0.0044565013 -0.0007320848 -0.0043702715
## [4,] -0.0008563857 -0.004280642 -0.0007320848 0.0071316218 -0.0009105724
## [5,] -0.0010981170 -0.004628883 -0.0043702715 -0.0009105724 0.0116082610
##
## Sample size (to estimate the mean)
## [1] 4321.355
##
## Sample size (to estimate the variance)
## [1] 1855.853
##
## Sample size (to estimate the kurtosis)
## [1] 2414.679
##
## L2 discrepancy
## [1] 0.01146337
##
## Sample size (per variable)
## [1] 2575.034 2884.157 2887.606 2446.961 3243.505
Figure 6
To compare \(\beta_4\) and \(\beta_5\).
Imputation
##
## INLA-IS
##
## Posterior means:
## [1] 26.51511 28.39077 26.26560 22.03728 26.63045 27.00209 26.45522 26.49309
## [9] 26.59322
##
## Posterior covariance:
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 71.0397200 -0.90698063 -2.8133053 0.0326676 1.56609937 1.7629186
## [2,] -0.9069806 33.50439599 -0.4254917 -1.4916191 -0.26614125 -0.2938505
## [3,] -2.8133053 -0.42549170 65.2925397 0.3148071 -2.49085355 -5.4279263
## [4,] 0.0326676 -1.49161909 0.3148071 36.8018981 -1.06252575 -0.7205948
## [5,] 1.5660994 -0.26614125 -2.4908535 -1.0625257 74.81998516 1.2181388
## [6,] 1.7629186 -0.29385050 -5.4279263 -0.7205948 1.21813881 65.6811630
## [7,] -1.6296688 0.02653053 0.1897709 -0.1358322 -0.44410856 0.6933812
## [8,] -0.0737553 -0.51698590 1.5222598 -3.1396391 -1.57803490 -0.7925197
## [9,] -1.5093999 -0.66050618 1.2404515 0.9071227 -0.04322918 1.1478514
## [,7] [,8] [,9]
## [1,] -1.62966880 -0.0737553 -1.50939986
## [2,] 0.02653053 -0.5169859 -0.66050618
## [3,] 0.18977088 1.5222598 1.24045148
## [4,] -0.13583225 -3.1396391 0.90712267
## [5,] -0.44410856 -1.5780349 -0.04322918
## [6,] 0.69338115 -0.7925197 1.14785139
## [7,] 67.77608604 0.4406005 0.37192544
## [8,] 0.44060051 70.5766706 -2.37564273
## [9,] 0.37192544 -2.3756427 67.63923850
##
## Sample size (to estimate the mean)
## [1] 3100.308
##
## Sample size (to estimate the variance)
## [1] 121.7308
##
## Sample size (to estimate the kurtosis)
## [1] 224.2479
##
## L2 discrepancy
## [1] 0.01491806
##
## Sample size (per variable)
## [1] 2839.153 2891.262 2686.612 3027.797 2579.964 3105.985 2778.729 3090.489
## [9] 2824.518##
## INLA-AMIS
##
## Posterior means:
## [1] 26.46663 28.23594 26.63339 21.86560 26.62650 26.70178 26.38388 26.58096
## [9] 26.46127
##
## Posterior covariance:
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 71.5548043 0.4202454 -0.2931976 0.2243021 0.19380847 0.3500978
## [2,] 0.4202454 30.5179421 -0.6198818 -1.5105641 1.04390174 -1.5939731
## [3,] -0.2931976 -0.6198818 70.6144808 0.4178743 -0.88192054 -0.8256479
## [4,] 0.2243021 -1.5105641 0.4178743 35.7855810 -0.67851751 0.1383889
## [5,] 0.1938085 1.0439017 -0.8819205 -0.6785175 70.49588285 0.5968602
## [6,] 0.3500978 -1.5939731 -0.8256479 0.1383889 0.59686018 69.7827746
## [7,] -0.9864415 -0.1514551 0.2957732 -0.3499932 -0.95516741 -0.8938459
## [8,] 0.4469601 0.2661267 0.5139215 0.8267749 0.04639142 0.3723948
## [9,] -0.1513927 -0.7321365 -0.2532585 0.8814391 -0.52955914 -0.3175650
## [,7] [,8] [,9]
## [1,] -0.9864415 0.44696013 -0.1513927
## [2,] -0.1514551 0.26612671 -0.7321365
## [3,] 0.2957732 0.51392145 -0.2532585
## [4,] -0.3499932 0.82677492 0.8814391
## [5,] -0.9551674 0.04639142 -0.5295591
## [6,] -0.8938459 0.37239477 -0.3175650
## [7,] 70.7372096 -0.23780864 0.5304446
## [8,] -0.2378086 70.89294968 -0.5518654
## [9,] 0.5304446 -0.55186537 69.0829550
##
## Sample size (to estimate the mean)
## [1] 9222.442
##
## Sample size (to estimate the variance)
## [1] 5586.245
##
## Sample size (to estimate the kurtosis)
## [1] 7123.592
##
## L2 discrepancy
## [1] 0.002903645
##
## Sample size (per variable)
## [1] 8270.826 8869.580 8433.700 8293.174 8468.784 8305.974 8178.022 8356.378
## [9] 8325.947
PQR
##
## INLA-IS
##
## Posterior means:
## [1] 13.65582 -10.18185
##
## Posterior covariance:
## [,1] [,2]
## [1,] 0.3476949 -0.4383091
## [2,] -0.4383091 0.5693098
##
## Sample size (to estimate the mean)
## [1] 1770.082
##
## Sample size (to estimate the variance)
## [1] 356.7213
##
## Sample size (to estimate the kurtosis)
## [1] 453.3711
##
## L2 discrepancy
## [1] 0.0215626
##
## Sample size (per variable)
## [1] 1657.741 1582.558##
## INLA-AMIS
##
## Posterior means:
## [1] 13.67884 -10.20970
##
## Posterior covariance:
## [,1] [,2]
## [1,] 0.3570757 -0.4491305
## [2,] -0.4491305 0.5812461
##
## Sample size (to estimate the mean)
## [1] 6340.138
##
## Sample size (to estimate the variance)
## [1] 5520.324
##
## Sample size (to estimate the kurtosis)
## [1] 5711.095
##
## L2 discrepancy
## [1] 0.007597714
##
## Sample size (per variable)
## [1] 6312.414 6298.910
